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SYLLABUS OF THE EXAMINATION
PAPER-I
MATHEMATICS
(Code No. 01)
(Maximum Marks- 300)
1. ALGEBRA
Concept of a set, operations on sets, Venn
diagrams. De Morgan laws. Cartesian product, relation, equivalence relation.
Representation of real numbers on a line. Complex numbers - basic properties,
modulus, argument, cube roots of unity. Binary system of numbers. Conversion of
a number in decimal system to binary system and vice-versa. Arithmetic,
Geometric and Harmonic progressions. Quadratic equations with real
coefficients. Solution of linear inequations of two variables by graphs.
Permutation and Combination. Binomial theorem and its applications. Logarithms
and their applications.
2. MATRICES AND DETERMINANTS :
Types of matrices, operations on matrices.
Determinant of a matrix, basic properties of determinants. Adjoint and inverse
of a square matrix, Applications - Solution of a system of linear equations in
two or three unknowns by Cramer's rule and by Matrix Method.
3. TRIGONOMETRY :
Angles and their measures in degrees and in
radians. Trigonometrical ratios. Trigonometric identities Sum and difference
formulae. Multiple and Sub-multiple angles. Inverse trigonometric functions.
Applications - Height and distance, properties of triangles.
4. ANALYTICAL GEOMETRY OF TWO AND THREE DIMENSIONS
:
Rectangular Cartesian Coordinate system. Distance
formula. Equation of a line in various forms. Angle between two lines. Distance
of a point from a line. Equation of a circle in standard and in general form.
Standard forms of parabola, ellipse and hyperbola. Eccentricity and axis of a
conic. Point in a three dimensional space, distance between two points.
Direction Cosines and direction ratios. Equation of a plane and a line in various
forms. Angle between two lines and angle between two planes. Equation of a
sphere.
5. DIFFERENTIAL CALCULUS :
Concept of a real valued function - domain, range
and graph of a function. Composite functions, one to one, onto and inverse
functions. Notion of limit, Standard limits - examples. Continuity of functions
- examples, algebraic operations on continuous functions. Derivative of
function at a point, geometrical and physical interpretation of a derivative -
applications. Derivatives of sum, product and quotient of functions, derivative
of a function with respect to another function, derivative of a composite
function. Second order derivatives. Increasing and decreasing functions.
Application of derivatives in problems of maxima and minima.
6. INTEGRAL CALCULUS AND DIFFERENTIAL EQUATIONS :
Integration as inverse of differentiation,
integration by substitution and by parts, standard integrals involving
algebraic expressions, trigonometric, exponential
and hyperbolic functions. Evaluation of definite
integrals - determination of areas of plane regions bounded by curves -
applications. Definition of order and degree of a differential equation,
formation of a differential equation by examples. General and particular
solution of a differential equations, solution of first order and first degree
differential equations of various types - examples. Application in problems of
growth and decay.
7. VECTOR ALGEBRA :
Vectors in two and three dimensions, magnitude and
direction of a vector. Unit and null vectors, addition of vectors, scalar
multiplication of a vector, scalar product or dot product of two vectors.
Vector product or cross product of two vectors. Applicationswork done by a
force and moment of a force and in geometrical problems.
8. STATISTICS AND PROBABILITY:
Statistics : Classification of data, Frequency
distribution, cumulative frequency distribution - examples. Graphical
representation - Histogram, Pie Chart, frequency polygon - examples. Measures
of Central tendency - Mean, median and mode. Variance and standard deviation -
determination and comparison. Correlation and regression.
Probability : Random experiment, outcomes and
associated sample space, events, mutually exclusive and exhaustive events,
impossible and certain events. Union and Intersection of events. Complementary,
elementary and composite events. Definition of probability - classical and
statistical - examples. Elementary theorems on probability - simple problems.
Conditional probability, Bayes' theorem - simple problems. Random variable as
function on a sample space. Binomial distribution, examples of random
experiments giving rise to Binominal distribution.
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